Adaptive labeling of network graphs

ABSTRACT

For each vertex of a network graph that includes a set of vertices, a meta-property of the vertex is determined relative to other vertices of the set of vertices, a distance of the vertex from a user&#39;s viewpoint of a three-dimensional (3D) rendering of the network graph is determined, and a ranking figure is calculated as a function of the determined meta-property in combination with the determined distance. The set of vertices of the network graph is ranked as a function of the respective calculated ranking figures. Labels for a subset of the set of vertices are selectively displayed on a display as a function of the ranking.

BACKGROUND

The present invention relates to computer performance improvements forreal-time network graph rendering. More particularly, the presentinvention relates to adaptive labeling of network graphs.

A three-dimensional (3D) graph may include multiple different verticesthat are distributed and connected in a 3D arrangement. The connectionsbetween the vertices are termed edges.

SUMMARY

A computer-implemented method includes, by a processor, for each vertexof a network graph that includes a plurality of vertices: determining ameta-property of the vertex relative to other vertices of the pluralityof vertices; determining a distance of the vertex from a user'sviewpoint of a three-dimensional (3D) rendering of the network graph;and calculating a ranking figure as a function of the determinedmeta-property in combination with the determined distance. Thecomputer-implemented method further includes the processor: ranking theplurality of vertices of the network graph as a function of therespective calculated ranking figures; and selectively displaying, on adisplay, labels for a subset of the plurality of vertices as a functionof the ranking.

A system that performs the computer-implemented method and a computerprogram product that causes a computer to perform thecomputer-implemented method are also described.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example of an implementation of a systemfor adaptive labeling of network graphs according to an embodiment ofthe present subject matter;

FIG. 2 is a block diagram of an example of an implementation of a coreprocessing module capable of performing adaptive labeling of networkgraphs according to an embodiment of the present subject matter;

FIG. 3 is a flow chart of an example of an implementation of a processfor adaptive labeling of network graphs according to an embodiment ofthe present subject matter;

FIG. 4A is a flow chart of an example of an implementation of initialprocessing within a process for iterative real-time adaptive labeling ofnetwork graphs to iteratively rank individual vertices according tometa-properties that have been selected for labeling according to anembodiment of the present subject matter; and

FIG. 4B is a flow chart of an example of an implementation additionalprocessing within a process for iterative real-time adaptive labeling ofnetwork graphs to select which ranked vertices to label, and tocalculate and render labels for selected vertices according to anembodiment of the present subject matter.

DETAILED DESCRIPTION

The examples set forth below represent the necessary information toenable those skilled in the art to practice the invention and illustratethe best mode of practicing the invention. Upon reading the followingdescription in light of the accompanying drawing figures, those skilledin the art will understand the concepts of the invention and willrecognize applications of these concepts not particularly addressedherein. It should be understood that these concepts and applicationsfall within the scope of the disclosure and the accompanying claims.

The subject matter described herein provides adaptive labeling ofnetwork graphs. Large network graphs may include vertex counts on theorder of hundreds of thousands to millions of interconnected verticesarranged in a three-dimensional (3D) arrangement, and interconnected byedges. The data represented at the respective vertices may change inreal time. A network graph may be displayed via a user interface of acomputing device, and computing device users may manipulate userinterface (UI) controls to initiate real-time changes to the renderedorientation, scale, and quantity of the rendered 3D vertices of thenetwork graphs. These real-time UI changes include factors such as theuser zooming in, zooming out, scrolling, moving, and otherwise adjustingeither locations or a quantity of vertices that are displayed.

It was observed that these types of real-time data and user interfacechanges impose computer processing demands related to real-timerendering of large 3D network graphs. Further, generation of real-time3D output renderings of all or a portion of a large network graph issubject to real-time computational and rendering performance constraintsof the underlying computing platform/device on which the network graphsare rendered. These real-time computational and rendering performanceconstraints include factors such as central processing unit (CPU)architecture and operating speed as they relate to CPU capacity andoccupancy/load; display resolution and display refresh capabilities andrefresh periodicity/rate of the output display device; and otherreal-time computer processing constraints.

The present technology solves recognized computer computational anddisplay output performance problems associated with calculating andrendering labels for large 3D network graphs. The present technologysolves these problems by providing a new form of computationalprocessing for programmatic determination and selection of whichvertices of a 3D network graph to label. The determination of whichvertices to label is based upon a two-dimensional (2D) user perspectiverelative to user-initiated real-time changes to 3D rendered orientationsof vertices of the 3D network graph and real-time changes to theunderlying data associated with the rendered vertices.

The technology described herein adapts to real-time computational anddisplay output performance impacts that result from real-timeuser-initiated and underlying data changes. Computer automation isdescribed herein that adapts both the calculation and display of labelsof vertices to user-initiated real-time changes to the 3D renderedorientations of the vertices and to any underlying real-time datachanges of the vertices. Computational processing for labeling verticesmay be further adapted to computer performance impacts associated withcalculating and rendering of labels as a magnitude of user-initiatedreal-time changes of orientation and real-time changes of underlyingdata of the vertices adjust real-time computational demands. Theselection of which vertices to label responsive to these real-timechanges may be further enhanced by computational calculation of 3Ddistances of vertices relative to a calculated or designated “viewpoint”that approximates a viewing location of the user. It is understood that,for purposes of the description herein, the “viewpoint” of the user or“user's viewpoint” is a specified 3D location relative to the 3D networkgraph that does not necessarily coordinate with a feature of aparticular user, but is instead a location/point at which a set ofvectors that each project from a respective vertex of the 3D model focusand terminate for purposes of the calculations described herein.

Accordingly, as the underlying data of the vertices themselves changedynamically over time, and further as a user modifies a displayorientation or perspective of the 3D network graph, performance of thecomputational processing for calculating and display processing forrendering labels may be monitored and managed to improve renderingperformance of the computer. Labels for a subset of the vertices may beselectively displayed to avoid computer performance degradation thatwould otherwise interfere with the user experience. The technologydescribed herein resolves previous technical computer performanceproblems, such as computer performance degradation, label or other imageflicker, overwhelmed output views with labels overlapping to an extentof being crowded beyond viewer comprehension, and viewer cognitiveoverload. As described herein, the present technology improvesoperational processing capabilities of the computing device itself andimproves the user interface of computing devices that are tasked withrendering 3D network graphs.

Some terminology used in describing some embodiments of the presentinvention will now be explained. A “network graph” is hereby defined asan inter-related set of elements that represent entities andrelationships between the entities. For example, the entities mayinclude people, building structures, town/cities, applications forservices or employment, financial transactions, insurance claims,documents that detail automobile accidents, and other elements that areinter-related by a computer process or that are physically inter-relatedaccording to a formalized relationship (e.g., family members, fellowemployees, etc.). Many different types of entities may be representedwithin a single network graph, and a single network graph may representthousands up to millions of entities. Network graphs are used bycomputers to process the respective entities and relationships in amanner that is well-suited to efficient computational analysis ofpossible roles, relative importance, and interactions of and between theentities represented in the graph; where such analysis would otherwiserequire prohibitive amounts of computational processing if networkgraphs were not used because of the magnitude of the number of entitiesthat are represented.

Network graphs typically include multiple “vertices.” A vertex is herebydefined as a computer representation of an entity that forms an elementof a network graph (e.g., a person, a building structure, a city/town, afinancial transaction, etc.). A vertex typically has one or more“property(ies),” and typically has one or more “meta-property(ies).” Thelabel-ranking calculations described herein may use one or moreproperties, one or more meta-properties (e.g., “degree,” as definedbelow), or any combination of properties and meta-properties asappropriate for the respective calculation.

A property of a vertex is hereby defined as an attribute of therepresented entity. A property is used to store the value of anattribute of the entity represented by the vertex. Some examples oftypes of properties for represented persons may include: (i) age; (ii)height; (iii) level of education; (iv) income; (v) employer; (vi)parent(s); (vii) siblings; (viii) child(ren); and other factors asappropriate for a given implementation. Some examples of types ofproperties for represented building structures may include: (i) size;(ii) dimensions; (iii) building materials; (iv) age of structure; (v)property value; (vi) zoning district; (vii) pending zoning actions; andother factors as appropriate for a given implementation. Some examplesof types of properties for represented towns/cities may include: (i)population; (ii) demographics; (iii) variations in education levelsacross residents; (iv) distances to major universities from a town/citycenter; (v) number of homes in a historic district; (vi) number ofparks; (vii) percentage of town/city devoted to parks and recreation forresidents; (viii) tax base; (ix) tax rate; and other factors asappropriate for a given implementation.

A meta-property of a vertex is hereby defined as a contextual orcomputed factor of the vertex (or represented entity) relative to othervertices and/or edges in the graph. A meta-property is information thatis not directly attributable to the represented entity (for a vertex) orrelationship (for an edge). A meta-property is information that may becalculated from analyzing the vertex/edge within the context of therepresented entities or is information that relates to the way that thedata of a vertex/edge was created/curated. Some examples of types ofmeta-properties for a vertex may include: (i) number of incident edges(degree); (ii) distance from some other identified vertex in the graph;(iii) a measure of the centrality of a vertex (e.g. the “betweenness” ofthe vertex); (iv) the shortest path from the vertex to some other(known) point in the graph; and other factors as appropriate for a givenimplementation.

Vertices of a network graph may be interconnected by “edges” within thenetwork graph. An edge is hereby defined as a computer representation ofa relationship between entities represented by vertices of a networkgraph. In view of the different types of elements represented within anetwork graph, the relationships between the entities a network graphare heterogeneous in nature. Some examples of edges may include: (i)inter-relationships between persons (e.g., parent-child relationships);(ii) inter-relationships between persons and building structures (e.g.,persons that live in a dwelling); (iii) inter-relationships betweentowns/cities (e.g., roads, waterways, etc.); and otherinter-relationships as appropriate for a given implementation.

Vertices and edges may be labeled by generation and rendering of a“label” that displays a selected set of properties and/ormeta-properties. Some examples of labels may include: (i) name:age; (ii)name:age:education; (iii) name:parent; (iii) city:population; and othercombinations of properties and/or meta-properties as appropriate for agiven implementation.

The technology described herein operates by, for each vertex of anetwork graph that includes a set of vertices: determining ameta-property of the vertex relative to other vertices of the set ofvertices, determining a distance of the vertex from a user's viewpointof a 3D rendering of the network graph, and calculating a ranking figureas a function of the determined meta-property in combination with thedetermined distance. The set of vertices of the network graph is rankedas a function of the respective calculated ranking figures. Labels for asubset of the set of vertices are selectively displayed on a display asa function of the ranking.

Alternatively, a method of displaying a three dimensional rendering of anetwork graph that includes multiple vertices may include: for eachvertex, determining a meta-property for the vertex relative to the othervertices, determining the distance of the vertex from a user's viewpointof the three dimensional rendering, and, calculating a ranking figure asa function of the inverse of the square of the determined meta-propertydivided by the square of the determined distance; ranking vertices ofthe network graph as a function of the corresponding calculated rankingfigures; and selectively displaying labels for a subset of the verticesas a function of the ranking.

Accordingly, the problem of improving label rendering computationalprocessing of a very large 3D graph may be solved by determining,according to a selected meta-property for which labels are to bedisplayed and based upon a rendered orientation of the 3D graph, adistance of each of a plurality of vertices from a viewpoint; andselectively displaying labels for any vertices with data that satisfiesthe selected meta-property and that are within a configured distance ofthe viewpoint.

The technology described herein performs a dynamic ranking of verticesby which vertex scores are computed every video frame time on a basis ofexisting properties or meta-properties of a subset of the vertices to berendered during the video frame, and on a basis of a relative proximityof each vertex in the subset of vertices to be rendered to the viewer.The vertex scores are utilized to determine, of the subset of verticesthat are to be rendered, which of this subset of vertices are to belabeled during the current video frame. As such, vertices that arecloser to the viewpoint may not be labeled, while vertices further awaymay be labeled according to their respective rankings, again based uponthe respective properties or meta-properties of the vertices andavailable real-time processing capabilities of the computing platform.Further, the underlying properties and meta-properties of the verticesthemselves may change dynamically over time and across different videoframes, and as a result, vertices that are labeled may change accordingto changed rankings.

In view of these technical aspects of the computational processingdescribed herein, the technology described herein differs fromconventional technologies in several respects. The technology describedherein is directed to determining whether to label individual verticesaccording to their respective rankings in view of available real-timecomputing capabilities and performance requirements utilized for labelrendering. The technology described herein is not directed todetermining where to place labels in rendered output or to rendering allpossible labels according to a zoom scale, each as performed inconventional mapping technologies. In further contrast to conventionallabeling technologies, because the labels as described herein arederived from the properties or meta-properties of the vertices that maychange over consecutive video frames, the rendered labels generated asdescribed herein are distinct from identifiers of represented elements,such as static geographic/location identifiers (e.g., towns, cities,road names, etc.), and are different from categorizations, clusterconnotations, or other forms of element identifiers. Further, thedistances that are utilized as described herein represent distances ofvertices in the subset of vertices to be rendered relative to aviewpoint and are not index-type distances by which vertices may betraversed and/or accessed relative to one another within a graph.

For purposes of the real-time processing described herein, there is auser controllable viewpoint within the 3D space relative to the 3D modelfrom which the 3D model may be viewed. The view of the 3D model from theviewpoint may be projected by use of graphics libraries onto a 2D image,which may then be displayed on a computer screen. Each vertex of a 3Dnetwork graph may be considered to have a defined and potentiallyvariable position in the 3D model of the graph. Additionally, a 3Dvector from a position of a vertex to the location of the viewpoint mayalso be defined and may be considered variable in direction andmagnitude. The magnitude of this 3D vector is the distance of the vertexfrom the viewpoint. Vertices may move due to dynamic modification oftheir properties or meta-properties, may move as a result of dynamicrevision of the graph layout, may move due to changes in other verticesor edges, or may move due to updates by the dynamic layout algorithm.Further, a user may initiate real-time changes in the position and/ororientation of the viewpoint relative the 3D network graph. As a resultof these various factors, the distance from a vertex to the viewpointmay change dynamically. The 3D distance of a vertex from the viewpointmay be used as a measure of proximity of the vertex to the center ofattention of the user.

The processing described herein may operate in real time on a displayrefresh boundary, and may perform computational processing within eachdisplay refresh interval to determine which vertices to label or removelabels from for the next display refresh of the network graph output. Itis understood that output display devices may update at differentrefresh rates by which the entire output or a portion of the display maybe re-rendered, and changes to the rendered data may be output. Displayupdate rate may be considered by reference to frame rate of videocontent, where it is recognized that approximately twenty-four (24)frames per second should be displayed to achieve an appearance of fluidmotion of moving objects. Example refresh rates of output displaydevices include twenty-four (24) frames per second, thirty (30) framesper second, sixty (60) frames per second, and potentially higher refreshrates as display technology advances.

Similarly, and for purposes of the present description, real timeperformance of output of a computer display device may be consideredaccording to an amount of time it takes to refresh an entire screen ofdata. As more data that has changed is designated to be rendered, itwill take longer for a computer to perform underlying labeldeterminations and generate output of a full-screen image.

To further detail the introductory description above, the presenttechnology was designed in recognition that a quantity of real-timechanges to underlying data of very large three-dimensional (3D) graphsmay increase to an extent that computing labels and rendering outputdata may be limited by computational and output capabilities of theunderlying computing platform. The technology described herein manages anumber of vertices for which real-time updates of displayed labels areperformed according to performance capabilities and real-timeperformance measurements of the underlying computing platform andproximity of the respective vertices to a user's viewpoint.

It was recognized that unbounded changes to rendering of labels mayinduce undesirable real-time output affects described above, such aslabel flickering where labels may turn on and/or off at the respectivedisplay refresh rate (e.g., 30 times per second). From a user interfaceperspective, these types of visual noise may be undesirable.

To avoid flicker of output labels that may otherwise result responsiveto the real-time UI or underlying vertex data changes described above,the technology described herein implements “bi-modal” hysteresis. Theterm bi-modal hysteresis as utilized herein represents a dual-mode ortwo-mode hysteresis, where decisions to label or remove a label are eachindividually processed according to independent and configurablehysteresis processing. Accordingly, where a vertex is located at aperipheral distance that may or may not be within the selected subset oflabeled vertices for each refresh cycle determination, label flicker maybe avoided by implementing a first “on” phase of hysteresis that beginswhen a label is first displayed to ensure that the label is displayedfor a minimum number of refresh cycles or for a minimum time period.Similarly, when a decision is made to no longer display a label, asecond “off” phase of hysteresis may be implemented to ensure that thelabel is not displayed for a minimum number of refresh cycles or for aminimum time. Again, these two modes of the bi-modal hysteresis areindependent, and each phase may be configured as appropriate for thegiven implementation. For example, the first “on” phase and the second“off” phase may be configured for equal amounts of time. Alternatively,either phase may be adjusted according to real-time demands ofprocessing, as appropriate for a given implementation. The terms“bi-model,” “dual-mode,” and “two-mode” shall be used interchangeablyherein with respect to hysteresis processing.

Regarding technical implementation of the subject matter describedherein, user interface (UI) selection options may be implemented toallow the user to select between various vertex labeling configurationsfor computer processing of labels. For example, the user may be able tochoose to label all vertices, which may be useful if the graph is smallenough or frame rate is not a concern to the particular user at theparticular time. Additionally, the user may be able to choose to label asubset of vertices according to a specified proportion, where theproportion provides a fixed real-time processing budget that may bespecified/used to label the most interesting or most significantvertices according to the data represented by the vertices. As anotheralternative, the user may be able to choose to label a subset ofvertices according to a specified frame-rate, where the number of labelsis varied (e.g., per frame) to sustain the frame rate and used to labelthe most interesting or most significant vertices according to the datarepresented by the vertices. Other alternatives are possible forselection of subsets of vertices according to performance-relatedmeasures, and all such possibilities are considered within the scope ofthe present description. The underlying computational processing forcalculation and rendering of labels may adapt to the UI selectionoptions as they are changed in real-time and may adapt to real-timefactors associated with calculation of labels according to complexitiesof the underlying data represented by the respective vertices.Additional CPU/processing budget within a given refresh frame time maybe used/configured by UI selection options to render additional labels,or the additional CPU/processing budget may be utilized for othercomputer processing tasks, as appropriate for a given implementation.Accordingly, the present technology adapts computational processing tothe complexities of the underlying data and does so responsively to userinterface demands of the user.

The vertices of a 3D graph may be ranked for significance (e.g., datasignificance) based upon a formula that by default computes an inverseof a square of a degree of a given vertex, divided by a square of adistance of the vertex from the viewer's 2D perspective/position in arendered 3D space. This formula may be adjusted as appropriate for agiven implementation.

These significance measures of the vertices may be interpreted by thecomputing device as a ranking of the vertices. The “degree” of a vertexmay be considered a meta-property of the vertex. As such, the degree ormeta-property of a vertex is not a direct property or attribute of theentity modeled by the vertex but is instead a computed metric thatreflects some other (meta) information about the vertex. Othermeta-properties or metrics may be used, including (but not limited to)any centrality measures of the vertex, or any statistic related to avertex relative to some set of all vertices for example. Thesignificance formula may be changed by changing the indices (and hencethe effect) of the constituent parts (e.g., distance, degree, or othermeta-property) or by introducing different properties or meta-propertiesof the vertex (e.g., “population” if the type of vertex were “city” or“altitude” if the type of vertex were “mountain”). Many other variationson ranking data significance of vertices are possible, and all suchvariations are considered within the scope of the technology describedherein.

With the individual vertex rankings calculated, the individual vertexrankings may be used to decide on a subset of vertices (if any) thatwill be labeled in accordance with the proportion or frame rate targetor budget, as set by the user interface option(s). The system renderingdevice/processor may then label as many of the ranked vertices aspossible within the specified target or budget.

Regarding implementation variations for the processing described above,the ranked vertices may be distributed across/within a series of bins orbuckets. The system may render labels for as many bins as possible,within the constraints of the specified target frame rate or budget.

Additionally, as introduced above with respect to the bi-modalhysteresis, a vertex that has been selected for labeling may continue tobe labeled for a specified/configured minimum duration, and a vertexthat has been removed from the labeled set may continue to have itslabel hidden (not be labeled) for a specified/configured minimumduration. These durations may be controllable by parameters associatedwith the implementation of the algorithm and may introduce the bi-modalhysteresis to reduce the sudden appearance and disappearance of labels,which may in turn reduce flicker. Vertices that are being displayed as aresult of this hysteresis may be selected for display before anyvertices from the ranked bins as selected.

By applying the adaptive labeling algorithm to a large network graph,the following outcomes may be achieved. The user may choose to havelabels on all objects. The user may choose to label objects in a sparsemanner, with emphasis on the vertices (or edges) that are most highlyranked (according to a user selectable set of parameters or properties).The sparseness may be controlled/specified by the user and may be usedto control computational processing to highlight key features of thenetwork graph. The user may choose to label objects to an extent thatdoes not affect the smoothness and responsiveness of the display output.As the user alters the viewpoint into the 3D rendered space, thevertices (or edges) nearest to the center of the user's attention may beemphasized more than vertices (or edges) further from the user'sattention, and as a result vertices (or edges) that are very distantfrom the viewer are less likely to be labeled. Accordingly, manycomputer performance improvements, output rendering performanceimprovements, and user interface usability improvements may be achievedby use of the technology described herein.

It should be noted that conception of the present subject matterresulted from recognition of certain limitations associated withperformance of computing devices tasked with rendering very large 3Dnetwork graphs. For example, it was observed that when displaying anetwork graph, it is beneficial to be able to display labels to help theuser to identify vertices and edges within the network graph. However,it was determined that rendering of labels is expensive in terms ofcomputer performance, and that when displaying a large graph (e.g.consisting of several thousand or more vertices) the performance impactof labeling results in render loop time violations and a reduction inachieved frame rate of the output device. It was determined that theseperformance impacts adversely affect the smoothness and responsivenessof the display, and lead to jerky and slow display screen updates. Itwas recognized that there is no known technique that manages thecomputational processor and display output load incurred by attemptingto label the vertices and/or edges of a large network graph. It was alsodetermined that prior strategies for selective labeling (e.g., of maps)would lead to arbitrary results and would generally not display the mostadvantageous set of labels for the graph. For example, general sampling(e.g., labeling every tenth object) or labeling the most significantobjects according to a zoomed perspective (e.g., labeling only cities ina zoomed out perspective of an online mapping application, but thenlabeling the smaller towns and roads as the user zooms in) do notadequately account for significance of data that is represented byvertices in and by a network graph (e.g., population, altitude, etc.).Further, it was determined that these types of selective labelingstrategies would omit display of labels for vertices that includesignificant data either because the given vertex is not in the sampleset (e.g., not a tenth element) or because the given vertex is not at aparticular perspective of a zoomed rendering, respectively. Thetechnology described herein solves these recognized problems byadaptively labeling a subset of the vertices (and optionally edges) thatare displayed, and extends this adaptive labeling to determining thesubset of labels that will be of most interest to the viewer accordingto the represented data when displaying a three-dimensional (3D)rendering of a network graph irrespective of a zoomed perspective of thenetwork graph. As introduced above, vertices that are closer to theviewpoint may not be labeled, while vertices further away may be labeledaccording to their respective rankings, again based upon the respectiveproperties or meta-properties of the vertices and available real-timeprocessing capabilities of the computing platform. The present subjectmatter improves performance of computing devices during real-timerendering of 3D network graphs by providing adaptive labeling of networkgraphs, as described above and in more detail below. As such, improvedcomputer performance may be obtained through use of the presenttechnology.

Computation of a vertex score may be performed in a variety of manners,as appropriate for a given implementation. The following portion of thepresent description provides several alternatives for computation of avertex score. It is understood that any of these variations may beutilized as appropriate for a given implementation.

The vertex score may be calculated as a function of the determinedmeta-property in combination with the determined distance. Severaloptions are available for calculating a vertex score. For example, thevertex score may be calculated as a square of the chosen meta-propertyvalue of the respective vertex divided by a square of the determineddistance of the vertex from the user's viewpoint of the 3D rendering ofthe network graph. Within this example, the higher-scoring vertices maybe considered to be higher ranking for purposes of label generation.Alternatively, and as an inverse to the option described above, thevertex score may be calculated as a square of the determined distance ofthe vertex from the user's viewpoint of the 3D rendering of the networkgraph divided by a square of the chosen meta-property value of therespective vertex. Within this example, the lower-scoring vertices maybe considered to be higher ranking for purposes of label generation. Itis understood that a value of one (1) may be added to the respectivedistance value or the respective chosen meta-property value to avoiddivision by zero (0). Other techniques for calculating a vertex scorethat reflects importance of the vertex in association with its distancefrom the viewpoint may be used, as appropriate for a givenimplementation. For example, a linear value, a square value, a cubevalue, or other modification of either the numerator or denominator maybe utilized. However, it has been determined that use of a square of thedistance and a square of meta-property delivered a visually stableresulting output. The vertex score, as calculated in a mannerappropriate for a given implementation, may be considered a rankingfigure by which to rank the selected vertex among other vertices, asdescribed above and in more detail below.

The following pseudo syntax examples utilize a set of abbreviations.First, “val” is “vertices already labeled” and contains a set ofvertices that are in positive hysteresis, such that display of labels iscontinued. Next, “vtl” is “vertices to label” and contains the rankedcandidate vertices that will be labeled if there is sufficient real-timeprocessing capacity to label these candidate vertices. Vertices that arein negative hysteresis are in a “held out” virtual set that is notmaterialized as a concrete set, but for which a count of vertices in theheld-out state is maintained as “vertices held out.”

The following pseudo syntax segments illustrate examples of possibleimplementations of certain technical details of the processing describedherein. The following first example pseudo syntax represents an earlyportion of per-frame processing, where the vertices may be sorted intosets, and bi-modal hysteresis may be applied to the vertices. Commentswithin this example pseudo syntax and the syntax itself provide thedescription of this example, and line numbers are provided inparentheses in the far-left column. Within this example, there is avariable “hysteresis” associated with each vertex. The value ofhysteresis is set to a configured maximum value when a vertex is firstlabeled or renewed for relabeling, and the value of hysteresis isdecremented at each frame cycle.

First Example Pseudo Syntax:

(1) // Vertices may be in one of three (3) states: (2) // * labeled andhysteresis > threshold (HYST_THR) (display label), (3) // * labeled andhysteresis between THR and minimum (HYST_MIN) (ignored) (4) // * or notlabeled (add to wait list) (5) if (hysteresis > labeller.HYST_THR) { //vertex is in hysteresis and labeled (6)    var val_entry = { }; (7)   val_entry.vid = vertex.id; (8)    val_entry.hyst = hysteresis; (9)   val.push(val_entry); (10) } (11) else if (hysteresis <labeller.HYST_THR) && hysteresis > labeller.HYST_MIN) { (12)    //Vertex is held out - does not get considered for relabeling untilHYST_MIN (13)    // is reached (14)    labeller.vertices_held_out =labeller.vertices_held_out+1,: (15) } (16) else { // THIS IS THEDECISION POINT WHERE THE VERTEX GETS A (17)    // CHANCE TO RENEW ITSLABEL BEFORE BEING HIDDEN (18)    // hyst is exactly THR or has reachedMIN: add vertex to list of those waiting (19) // to be labeled (20)   // This case of hyst equal THR provides a chance for the vertex toremain (21)    // displayed based on its significance, avoiding goinginto hold out state. (22)    var vtl_entry = { }; (23)    vtl_entry.vid= vertex.id; (24)    vtl_entry.distance = sig; (25)    vtl_entry.hyst =hysteresis; (26)    vtl.push(vtl_entry); (27) }

Within the first example pseudo syntax, values of “HYST_MAX,”“HYST_THR,” and “HYST_MIN” may be set to any values appropriate for agiven implementation. Example values for these variables may beHYST_MAX=10, HYST_THR=5, and HYST_MIN=0. Settings selected at thesevalues would have an effect of displaying each label for a minimum of 5frames (e.g., 10-5), and hiding each label for a minimum of 5 frames(e.g., 5-0). As such, this variation would provide symmetric bi-modalhysteresis because labels would be guaranteed to be displayed and hiddenfor equal numbers of frame counts. Alternatively, the bi-modalhysteresis may be implemented to be non-symmetrical by adjusting thevalues of the maximum and threshold hysteresis settings (e.g.HYST_MAX=12, HYST_THR=5, or otherwise as appropriate for a givenimplementation).

The following second example pseudo syntax may be performed later in theper-frame processing. This second example pseudo syntax illustratesprocessing for an adaptive mode of label display in which labels ofedges may also be displayed. It should be noted that the technologydescribed herein additionally allows a user, under user control, toenable a “neighborhood” labeling mode. Under the neighboring labelingmode, if a vertex is labeled, then its adjacent edges and immediateneighbor vertices are also labeled. This neighboring labeling modeprovides additional context within which the original subject vertex maybe viewed or interpreted. In adaptive labeling mode, the immediateneighbor vertices are not automatically labeled because they are subjectto the adaptive labeling algorithm, as described. However, each adjacentedge of a vertex may be labeled if labeling is enabled for the type ofthat edge. The following second example pseudo syntax also illustrates“bucketized” processing of vertices to improve real-time performance.Again, comments within this example pseudo syntax and the syntax itselfprovide the description of this example, and line numbers are providedin parentheses in the far left column.

Second Example Pseudo Syntax:

(1) // Display labels for VAL set (2) for (var v=0;v<this.vertices_already_labelled.length; v++) { (3)    var vtx_id =this.vertices-already_labelled[v].vid; (4)    var vertex =this.graph.getVertexById(vtx_id); (5) (6)    // Get the label for thetarget vertex (7)    var vtxLabel = null; (8)    vtxLabel =this.vertexLabel(vertex, this.graph); (9)    if (vtxLabel !== null) {(10)       this._displayVertexLabel(vertex, vtxLabel, ctx); (11) (12)      // In adaptive mode, label visible incident edges (only) iflabeling (13)       // is enabled (14)      this._displayVertexEdgeLabels(vertex, ctx); (15)    } (16) } (17)(18) // Display labels for as many candidate (ranked) vertices aspossible, up to the last (19) // bucket, referred to by “lb,” calculatedearlier in the processing (20) if (this.labeller_vbuckets.length > 0 ){(21)    for (var b=0; b<=lb; b++) { (22)       var bkt =this.labeller_vbuckets[b]; (23)       for (var j=0; j<bkt.length; j++) {(24)          var vtx_id = bkt[j]; (25)          var vertex =this.graph.getVertexById(vtx_id); (26) (27)          var mdl =this._getOrCreateLabellerMetadata(vertex); (28)          // Resethysteresis to max when vertex is first displayed (29)          // Min#frames to show label is HYST_MAX - HYST_THR (30)          // THEFOLLOWING IS WHERE THE HYSTERESIS (31)          // RESETS TO HYST_MAX(32)          mdl.hyst = this.HYST_MAX; (33) (34)          var vtxLabel= null; (35)          vtxLabel = this.vertexLabel(vertex, this.graph);(36)          if (vtxLabel !== null) { (37)            this._displayVertexLabel(vertex, vtxLabel, ctx);    (38)(39)             // In adaptive mode perform a subset of neighborhood(40)             // mode, labeling visible only the incident edges that(41)          // have labeling enabled (and not neighboring vertices)(42)             this._displayVertexEdgeLabels(vertex, ctx); (43)         } (44)       } (45)    } (46) (47)    // Manage the hysteresisfor vertices in this bucket (48)    for (var b=lb+1;b<this.labeller_num_buckets-1 ; b++) { (49)       var bkt =this.labeller_vbuckets[b]; (50)       for (var j=0; j<bkt.length; j++) {(51)          var vtx_id = bkt[j]; (52)          var vertex =this.graph.getVertexById(vtx_id); (53)          var mdl =this._getOrCreateLabellerMetadata(vertex); (54) (55)          if(mdl.hyst == this.HYST_THR) { (56)             // Set random backofftimer here by selecting random (57)             // fraction of THR.Vertex ranking will decrement (58)             // hysteresis until itreaches MIN (59)             mdl.hyst = Math.random( ) * this.HYST_THR;(60)             mdl.hyst = Math.floor(mdl.hyst); (61)          } (62)         else if (mdl.hyst == this.HYST_MIN) { (63)             //ignore the vertex. It is out of hysteresis but was not (64)            // chosen due to insufficient significance (65)          }(66)       } (67)    } (68) }

It may be noted that within the second example pseudo syntax above eachlabel is provided with a slightly randomized period in the negativephase of the bi-modal hysteresis relative to a hysteresis thresholdvalue (HTHR) (e.g., within the range HTHR>count>0). Randomizing thenegative phase of the bi-modal hysteresis may be utilized to avoidintroducing pulsating effects as numbers of labels are reintroduced inthe same frame.

The adaptive labeling of network graphs described herein may beperformed in real time to allow improved computing device performanceduring updating of network graphs. For purposes of the presentdescription, real time shall include any time frame of sufficientlyshort duration as to provide reasonable response time for informationprocessing acceptable to a user of the subject matter described.Additionally, the term “real time” shall include what is commonly termed“near real time”—generally meaning any time frame of sufficiently shortduration as to provide reasonable response time for on-demandinformation processing acceptable to a user of the subject matterdescribed (e.g., within a portion of a second or within a few seconds).These terms, while difficult to precisely define are well understood bythose skilled in the art.

FIG. 1 is a block diagram of an example of an implementation of a system100 for adaptive labeling of network graphs. A computing device_1 102through a computing device_N 104 communicate via a network 106 withseveral other devices. The other devices include a server_1 108 througha server_M 110, and a database 112. Each of the server_1 108 through theserver_M 110 and the database 112 may provide for storage and retrievalof network graphs within the system 100. Each of these devices may beconsidered a “computing platform” for ease of reference and descriptionherein.

As will be described in more detail below in association with FIG. 2through FIG. 4B, the computing device_1 102 through the computingdevice_N 104 may each provide automated adaptive labeling of networkgraphs. The server_1 108 through the server_M 110 may also provideautomated adaptive labeling of network graphs. The automated adaptivelabeling of network graphs is based upon real-time evaluation ofcomputer performance of a computing platform in response to userinterface (UI) changes of orientation (e.g., zooming, scrolling, etc.)and in response to changes of underlying data and meta-properties ofvertices of network graphs. The adaptive labeling of network graphsselectively renders labels (and optionally edges) of network graphsaccording to performance capabilities of the underlying monitoredcomputing platform that is rendering the network graph. The adaptivelabeling of network graphs may improve the real-time performance of thecomputing platform without degradation of and while enhancing the userinterface experience and usability. The present technology may beimplemented at a user computing device or server device level, or by acombination of such devices as appropriate for a given implementation. Avariety of possibilities exist for implementation of the present subjectmatter, and all such possibilities are considered within the scope ofthe present subject matter.

The network 106 may include any form of interconnection suitable for theintended purpose, including a private or public network such as anintranet or the Internet, respectively, direct inter-moduleinterconnection, dial-up, wireless, or any other interconnectionmechanism capable of interconnecting the respective devices.

The server_1 108 through the server_M 110 may include any device capableof providing data (e.g., network graphs and/or data of vertices of anetwork graph) for consumption by a device, such as the computingdevice_1 102 through the computing device_N 104, via a network, such asthe network 106. As such, the server_1 108 through the server_M 110 mayeach include a web server, application server, or other data serverdevice.

The database 112 may include a relational database, an object database,or any other storage type of device. As such, the database 112 may beimplemented as appropriate for a given implementation.

FIG. 2 is a block diagram of an example of an implementation of a coreprocessing module 200 capable of performing adaptive labeling of networkgraphs. The core processing module 200 may be associated with either thecomputing device_1 102 through the computing device_N 104 or with theserver_1 108 through the server_M 110, as appropriate for a givenimplementation. As such, the core processing module 200 is describedgenerally herein, though it is understood that many variations onimplementation of the components within the core processing module 200are possible and all such variations are within the scope of the presentsubject matter. Further, the core processing module 200 may beimplemented as an embedded processing device with circuitry designedspecifically to perform the processing described herein as appropriatefor a given implementation.

The core processing module 200 may provide different and complementaryprocessing for network graph rendering and computing device performanceimprovements in association with each implementation. As such, for anyof the examples below, it is understood that any aspect of functionalitydescribed with respect to any one device that is described inconjunction with another device (e.g., sends/sending, etc.) is to beunderstood to concurrently describe the functionality of the otherrespective device (e.g., receives/receiving, etc.).

A central processing unit (CPU) 202 (“processor”) provides hardware thatperforms computer instruction execution, computation, and othercapabilities within the core processing module 200. A display 204provides visual information to a user of the core processing module 200and an input device 206 provides input capabilities for the user.

The display 204 may include any display device, such as a cathode raytube (CRT), liquid crystal display (LCD), light emitting diode (LED),electronic ink displays, projection, touchscreen, or other displayelement or panel. The input device 206 may include a computer keyboard,a keypad, a mouse, a pen, a joystick, touchscreen, voice commandprocessing unit, or any other type of input device by which the user mayinteract with and respond to information on the display 204.

A communication module 208 provides hardware, protocol stack processing,and interconnection capabilities that allow the core processing module200 to communicate with other modules within the system 100. Thecommunication module 208 may include any electrical, protocol, andprotocol conversion capabilities useable to provide interconnectioncapabilities, as appropriate for a given implementation. As such, thecommunication module 208 represents a communication device capable ofcarrying out communications with other devices.

A memory 210 includes a three-dimensional (3D) network graph storagearea 212 that stores network graphs for processing and display inassociation with the core processing module 200. The memory 210 alsoincludes a label rendering processing storage area 214 that providescomputational processing space for calculation of distances, bi-modalhysteresis processing, label calculation from vertex meta-properties,and other computational processing as appropriate for a givenimplementation.

It is understood that the memory 210 may include any combination ofvolatile and non-volatile memory suitable for the intended purpose,distributed or localized as appropriate, and may include other memorysegments not illustrated within the present example for ease ofillustration purposes. For example, the memory 210 may include a codestorage area, an operating system storage area, a code execution area,and a data area without departure from the scope of the present subjectmatter.

A three-dimensional (3D) network graph label rendering module 216 isalso illustrated. The 3D network graph label rendering module 216provides computational processing for measurement of real-time displayoutput performance in conjunction with label rendering and foradjustment/adaptation of label rendering by the core processing module200, as described above and in more detail below. The 3D network graphlabel rendering module 216 implements the automated adaptive labeling ofnetwork graphs of the core processing module 200.

It should also be noted that the 3D network graph label rendering module216 may form a portion of other circuitry described without departurefrom the scope of the present subject matter. The 3D network graph labelrendering module 216 may form a portion of an interrupt service routine(ISR), a portion of an operating system, or a portion of an applicationwithout departure from the scope of the present subject matter. The 3Dnetwork graph label rendering module 216 may also include an embeddeddevice with circuitry designed specifically to perform the processingdescribed herein as appropriate for a given implementation.

A timer/clock module 218 is illustrated and used to determine timing(and date) information, such as display refresh timing and labelrendering process timing, as described above and in more detail below.As such, the 3D network graph label rendering module 216 may utilizeinformation derived from the timer/clock module 216 for informationprocessing activities, such as the adaptive labeling of network graphs.

The CPU 202, the display 204, the input device 206, the communicationmodule 208, the memory 210, the 3D network graph label rendering module216, and the timer/clock module 218 are interconnected via aninterconnection 220. The interconnection 220 may include a system bus, anetwork, or any other interconnection capable of providing therespective components with suitable interconnection for the respectivepurpose.

Though the different modules illustrated within FIG. 2 are illustratedas component-level modules for ease of illustration and descriptionpurposes, it should be noted that these modules may include anyhardware, programmed processor(s), and memory used to carry out thefunctions of the respective modules as described above and in moredetail below. For example, the modules may include additional controllercircuitry in the form of application specific integrated circuits(ASICs), processors, antennas, and/or discrete integrated circuits andcomponents for performing communication and electrical controlactivities associated with the respective modules. Additionally, themodules may include interrupt-level, stack-level, and application-levelmodules as appropriate. Furthermore, the modules may include any memorycomponents used for storage, execution, and data processing forperforming processing activities associated with the respective modules.The modules may also form a portion of other circuitry described or maybe combined without departure from the scope of the present subjectmatter.

Additionally, while the core processing module 200 is illustrated withand has certain components described, other modules and components maybe associated with the core processing module 200 without departure fromthe scope of the present subject matter. Additionally, it should benoted that, while the core processing module 200 is described as asingle device for ease of illustration purposes, the components withinthe core processing module 200 may be co-located or distributed andinterconnected via a network without departure from the scope of thepresent subject matter. Many other possible arrangements for componentsof the core processing module 200 are possible and all are consideredwithin the scope of the present subject matter. Accordingly, the coreprocessing module 200 may take many forms and may be associated withmany platforms.

FIG. 3 through FIG. 4B described below represent example processes thatmay be executed by devices, such as the core processing module 200, toperform the automated adaptive labeling of network graphs associatedwith the present subject matter. Many other variations on the exampleprocesses are possible and all are considered within the scope of thepresent subject matter. The example processes may be performed bymodules, such as the 3D network graph label rendering module 216 and/orexecuted by the CPU 202, associated with such devices. It should benoted that time out procedures and other error control procedures arenot illustrated within the example processes described below for ease ofillustration purposes. However, it is understood that all suchprocedures are considered to be within the scope of the present subjectmatter. Further, the described processes may be combined, sequences ofthe processing described may be changed, and additional processing maybe added or removed without departure from the scope of the presentsubject matter.

FIG. 3 is a flow chart of an example of an implementation of a process300 for adaptive labeling of network graphs. The process 300 representsa computer-implemented method of performing the subject matter describedherein. At block 302, the process 300 determines, for each vertex of anetwork graph that comprises a plurality of vertices, a meta-property ofthe vertex relative to other vertices of the plurality of vertices. Atblock 304, the process 300 determines, for each vertex of the networkgraph that comprises the plurality of vertices, a distance of the vertexfrom a user's viewpoint of a 3D rendering of the network graph. At block306, the process 300 calculates, for each vertex of the network graphthat comprises the plurality of vertices, a ranking figure as a functionof the determined meta-property in combination with the determineddistance. At block 308, the process 300 ranks the plurality of verticesof the network graph as a function of the respective calculated rankingfigures. At block 310, the process 300 selectively displays, on adisplay, labels for a subset of the plurality of vertices as a functionof the ranking.

FIGS. 4A-4B illustrate a flow chart of an example of an implementationof process 400 for iterative real-time adaptive labeling of networkgraphs. The process 400 represents a computer-implemented method ofperforming the subject matter described herein. FIG. 4A illustratesinitial processing within the process 400 to iteratively rank individualvertices of a set of vertices according to meta-properties that havebeen selected for labeling. FIG. 4B illustrates processing for selectionof which ranked vertices to label, and for calculation and rendering oflabels for selected vertices. The processing described in associationwith the process 400 occurs during each frame refresh period/cycle of anoutput display device that is tasked with rendering labels for large 3Dnetwork graphs.

With reference to FIG. 4A and decision point 402, the process 400 beginsiterative real-time processing, and makes a determination as to whetherto render a display frame output of a network graph, which may occur ata display refresh real-time boundary or interval, or other real-timeevent as appropriate for a given implementation. As described above,example display refresh periods may include twenty-four (24) frames persecond, thirty (30) frames per second, or other display refresh rate asappropriate for a given implementation.

It is understood that the data represented by vertices within a networkgraph may change in real-time and between display refreshperiods/intervals. As will be described in more detail below, theprocess 400 dynamically updates which of the set of vertices form asubset of the set of vertices for which labels are selectively displayedresponsive to real-time changes of the meta-properties of the verticesthat result from real-time changes in data represented by the respectivevertices within the network graph.

In response to determining at decision point 402 to render a displayframe output of a network graph, the process 400 begins iterativeprocessing to determine which vertices of the network graph to label andselects a first vertex of the network graph at block 404. At decisionpoint 406, the process 400 makes a determination as to whether vertexlabeling is enabled for the selected vertex. Affirmative processingresponsive to the determination at decision point 406 will be describedfurther below to initially describe the iterative per-vertex processingcycle of the process 400.

In response to determining that vertex labeling is not enabled for theselected vertex, the process 400 sets a hysteresis data variable (HYST)that controls processing of the selected vertex to a configured minimumhysteresis value (HMIN) at block 408. The process 400 makes adetermination at decision point 410 as to whether any additionalvertices of the network graph exist to be processed. Affirmativeprocessing responsive to the determination at decision point 410 will bedescribed further below to initially describe the iterative per-vertexprocessing cycle of the process 400.

In response to determining at decision point 410 that at least oneadditional vertex of the network graph exist to be processed, theprocess 400 returns to block 404 and selects the next vertex. Theprocess 400 iteratively processes each vertex of the network graph asdescribed above and as described in more detail below.

Returning to the description of decision point 406 and processingresponsive to an affirmative determination, in response to determiningat decision point 406 that vertex labeling is enabled for the selectedvertex, the process 400 makes a determination at decision point 412 asto whether the selected vertex of the network graph is currently visiblewithin the area of the display. As such, the process 400 may improveefficiency by discontinuing processing efforts for vertices that areoutside of a visible area of the rendered display output. In response todetermining at decision point 412 that the selected vertex of thenetwork graph is not currently visible within the area of the display,the process 400 returns to block 408 and sets the hysteresis datavariable (HYST) that controls processing of the selected vertex to theconfigured minimum hysteresis value (HMIN). The process 400 iterates asdescribed above.

Alternatively, in response to determining at decision point 412 that theselected vertex of the network graph is currently visible within thearea of the display, the process 400 makes a determination at decisionpoint 414 as to whether the hysteresis data variable (HYST) thatcontrols processing of the selected vertex greater than the minimumhysteresis value (HMIN). As described in detail further above, theprocess 400 may establish, as bi-modal display output hysteresis, afirst hysteresis phase that defines a minimum display time fordisplaying the labels for the subset of the set of vertices responsiveto the labels being displayed, and a second hysteresis phase thatdefines a minimum time for not displaying the labels for any of thesubset of the set of vertices responsive to the display of the labelsbeing stopped. The processing at decision point 412 and other decisionpoints described below implement this bi-modal hysteresis, and thebi-modal hysteresis may reduce real-time label display flickerresponsive to real-time changes of the meta-properties of the verticesaccording to the bi-modal display output hysteresis.

In response to determining at decision point 414 that the hysteresisdata variable (HYST) that controls processing of the selected vertex isgreater than the configured minimum hysteresis value (HMIN), the process400 decrements the hysteresis data variable (HYST) at block 416.Alternatively, in response to determining that the hysteresis datavariable (HYST) that controls processing of the selected vertex is notgreater than (e.g., less than or equal to) the minimum hysteresis value(HMIN) at decision point 414, or in response to decrementing thehysteresis data variable (HYST) at block 416, the process 400 retrievesa value (PVAL) of a chosen meta-property of the selected vertex at block418. As described above, meta-properties are computed metrics thatreflect (meta) information about the vertex, and any appropriatemeta-property may be chosen for use in calculation of labels forvertices. As such, the process 400 retrieves the specified/chosenmeta-property of the vertex for further processing. It is understoodthat more than one meta-property may be chosen for use in labelcalculations and processing, as appropriate for a given implementation.

At block 420, the process 400 computes a three-dimensional (3D) distance(D) of the vertex from current 3D coordinates of the viewpoint, asdefined above. This distance as computed may be used in the computationof a vertex score.

At block 422, the process 400 computes a vertex score of the selectedvertex. The vertex score may be calculated as a square of the chosenmeta-property value (PVAL) of the respective vertex divided by a squareof the determined distance (D) of the vertex from the user's viewpointof the 3D rendering of the network graph (e.g.,ranking/score=(PVAL*PVAL)/(D*D)). It is understood that a value of one(1) may be added to the distance value to avoid division by zero (0).Other techniques for calculating a vertex score that reflects importanceof the vertex in association with its distance from the viewpoint may beused, as appropriate for a given implementation. For example, a linearvalue, a square value, a cube value, or other modification of either thenumerator or denominator may be utilized. However, it has beendetermined that use of a square of the distance and a square ofmeta-property delivered a visually stable resulting output. The vertexscore, as calculated in a manner appropriate for a given implementation,may be considered a ranking figure by which to rank the selected vertexamong other vertices, as described above and in more detail below.

It is understood that the data and meta-properties represented byindividual vertices of a network graph, and the orientation and scale(e.g., zoom, etc.) requested for display by the user may change acrossframe refresh period/cycle boundaries. As such, the process 400 mayiteratively update the determined distance, the calculated rankingfigure, and the ranking of the vertices of the network graph responsiveto at least one user input instructing a change of the 3D rendering ofthe network graph and any changes to the underlying data ormeta-properties of the network graph, and the process 400 mayselectively display labels for an updated subset of the set of verticesas a function of the updated ranking on a display.

At decision point 424, the process 400 begins hysteresis processing andmakes a determination as to whether the hysteresis data variable (HYST)is greater than a hysteresis threshold value (HTHR) that controls vertexlabeling. In response to determining that the hysteresis data variable(HYST) is greater than the hysteresis threshold value (HTHR) (e.g., thatthe vertex is already labeled), the process 400 adds the selected vertexto a set of vertices that are already labeled (VAL_SET) at block 426,and the process 400 returns to decision point 410 and iterates asdescribed above.

Alternatively, in response to determining at decision point 424 that thehysteresis data variable (HYST) is not greater than the hysteresisthreshold value (HTHR) that controls vertex labeling, the process 400makes a determination at decision point 428 as to whether the hysteresisdata variable (HYST) is equal to the hysteresis threshold value (HTHR).Where hysteresis data variable (HYST) is equal to the hysteresisthreshold value (HTHR), the vertex gets a chance to renew its labelbefore being hidden, and the vertex may be labeled based upon itsscore/ranking relative to other vertices. As such, in response todetermining that the hysteresis data variable (HYST) is equal to thehysteresis threshold value (HTHR), the process 400 adds the vertex tothe set of vertices to label (VTL_SET) at block 430, and the process 400returns to decision point 410 and iterates as described above.Additional processing will be described further below to determine whichvertices of the set of vertices to label (VTL_SET) will actually belabeled during any given display refresh period.

Alternatively, in response to determining at decision point 428 that thehysteresis data variable (HYST) is not equal to the hysteresis thresholdvalue (HTHR), the process 400 makes a determination at decision point432 as to whether the hysteresis data variable (HYST) is between to thehysteresis threshold value (HTHR) and the configured minimum hysteresisvalue (HMIN). In this state of hysteresis, the selected vertex is notlabeled, and is maintained in a not labeled state to avoid labelflicker. In response to determining that the hysteresis data variable(HYST) is between to the hysteresis threshold value (HTHR) and theconfigured minimum hysteresis value (HMIN), the process 400 incrementsthe vertices held out processing counter (vertices held out) at block434, and the process 400 returns to decision point 410 and iterates asdescribed above.

As a final alternative in the hysteresis processing section, in responseto determining at decision point 432 that the hysteresis data variable(HYST) is not between to the hysteresis threshold value (HTHR) and theconfigured minimum hysteresis value (HMIN) (e.g., that the hysteresisequals the hysteresis minimum, HYST==HMIN), the process 400 adds thevertex to the set of vertices to label (VTL_SET) at block 436. As such,in response to the non-labeled hysteresis phase (e.g., negativehysteresis) being completed, the vertex also gets a chance to renew itslabel because the vertex label has been hidden long enough to satisfythe negative hysteresis setting, and the vertex may be labeled basedupon its score/ranking relative to other vertices. The process 400 againreturns to decision point 410 and iterates as described above

Returning to the description of decision point 410 and processingresponsive to an affirmative determination, in response to determiningat decision point 410 that no additional vertices of the network graphexist to be processed (e.g., that all vertices have been initiallyprocessed), the process 400 transitions to the processing shown anddescribed in association with FIG. 4B as represented by the circledletter “A” in FIG. 4A and FIG. 4B.

FIG. 4B illustrates additional processing associated with the process400 for iterative real-time adaptive labeling of network graphs andincludes additional processing to select which ranked vertices to label,and to calculate and render labels for selected vertices. At block 438,the process 400 begins processing for selection of which ranked verticesto label, and for calculation and rendering of labels for selectedvertices by calculating a number of candidate vertices to label(CANDIDATES). For purposes of example, the number of candidate verticesto label may be calculated as the set of vertices already labeled(VAL_SET) plus the set of vertices to label (VTL_SET) (e.g.,VAL_SET+VTL_SET). The number of candidate vertices to label may furtherbe based upon a current number of vertices of the network graph that arewithin a viewable area of a display and distance from the viewpoint, maybe based upon real-time processing requirements for calculation anddisplay of vertices, or may be based upon other factors as appropriatefor a given implementation.

At block 440, the process 400 calculates a population of vertices forpossible display. For purposes of example, the calculated population(POP) of vertices for possible display may be calculated as thecalculated number of candidates (CANDIDATES) multiplied by aconfigurable proportion (PROP), where the configurable proportion may bedynamically adjusted and smoothed over time based upon an achieveddisplay frame rate versus a target frame rate.

At block 442, the process 400 calculates a display budget for display ofvertex labels. For purposes of example, the calculated display budgetmay be calculated as the population (POP) number minus the number ofvertices in the set of vertices already labelled (VAL_SET) (e.g.,POP−VTL_SET). As such, the process 400 may dynamically adjust aproportion (e.g., quantity) of vertices for which the labels areselectively displayed according to a configured real-time computationalperformance criterion for display update processing. It should be notedthat for purposes of implementation, quantization buckets may beutilized and the budget may be distributed across a set of quantizationbuckets that each include sets of vertices for which labels may bedisplayed, and the calculated budget may be the number of quantizationbuckets of vertices for which to display labels.

At block 444, the process 400 displays labels for vertices in the set ofvertices already labelled (VAL_SET). Because these vertices are alreadylabelled, processing may be improved by displaying these labels firstbecause they are known to satisfy hysteresis requirements and real-timeprocessing may be reduced.

At block 446, the process 400 displays labels for vertices in the set ofvertices to label (VTL_SET). As each vertex in the set of vertices tolabel is labelled at block 446, the process 400 may also set thehysteresis data variable (HYST) that controls processing of therespective vertex to a configured maximum hysteresis value (HMAX) tobegin hysteresis processing of the respective vertex with the firstframe time during which the label for the vertex is displayed. Theprocess 400 may also label the incident edges of each labelled vertex atblock 446, as appropriate for a given implementation. The processing atblock 446 may continue up to a configured amount of time budget fordisplay of new labels during the current frame rendering period and therelated processing.

It should be noted that the process 400 may tune its processing forrendering of labels across iterative frame times relative to an achievedframe rate to either increase or decrease a quantity of vertices forwhich labels are rendered. The process 400 may monitor an achievedreal-time computational performance of display update processingrelative to a threshold real-time computational performance criterionfor display update processing. The threshold real-time computationalperformance criterion for display update processing may include anamount of time consumed to calculate and/or refresh labels that arerendered, a number of processor clock cycles consumed to calculateand/or refresh labels that are rendered, or other criteria by whichperformance may be measured. In response to the monitoring, the process400 may increase a proportion (e.g., quantity) of vertices for which thelabels are selectively displayed until the achieved real-timecomputational performance approximates the threshold real-timecomputational performance criterion (e.g., budget) responsive todetermining that real-time computational performance exceeds a thresholdreal-time computational performance criterion (e.g., budget). Anyvertices for which labels were not rendered may have a chance to belabelled in the next frame period and iteration of the process 400.Consistent with the description above, the process 400 may reduce theproportion (e.g., quantity) of the vertices for which the labels areselectively displayed until the achieved real-time computationalperformance approximates the threshold real-time computationalperformance criterion. Any vertices for which labels were rendered thatcaused the frame budget and performance to be excessively reduced may beremoved from labeling in a subsequent frame period during which theirrespective hysteresis count values have reached the configured minimumhysteresis value (HMIN), as the process 400 iterates.

The process 400 begins iterative processing of individual vertices inthe subset of remaining vertices to label to randomize the remaininghysteresis for label display of this subset to avoid coincident changesin label rendering. At block 448, the process 400 selects a vertex fromthe subset of remaining vertices to label. At decision point 450, theprocess 400 makes a determination as to whether the hysteresis datavariable (HYST) that controls processing of the selected vertex equalsthe configured hysteresis threshold value (HTHR). In response todetermining that the hysteresis data variable (HYST) that controlsprocessing of the selected vertex equals the configured hysteresisthreshold value (HTHR), the process randomizes the hysteresis datavariable (HYST) of the selected vertex to a value between the hysteresisthreshold value (HTHR) and configured minimum hysteresis value (HMIN) atblock 452. In response to completion of the randomization of thehysteresis data variable (HYST) of the selected vertex at block 452, orin response to determining at decision point 450 that the hysteresisdata variable (HYST) that controls processing of the selected vertexdoes not equal the configured hysteresis threshold value (HTHR), theprocess 400 makes a determination at decision point 454 as to whetherprocessing to randomize the individual vertices in the subset ofremaining vertices to label has been completed. In response todetermining that the processing to randomize the individual vertices inthe subset of remaining vertices to label has not been completed, theprocess 400 returns to block 448 and selects the next remaining vertex.Alternatively, in response to determining that the processing torandomize the individual vertices in the subset of remaining vertices tolabel has been completed, the process 400 transitions and returns to theprocessing shown and described in association with FIG. 4A at decisionpoint 402, as represented by the circled letter “B” in FIG. 4B and FIG.4A.

As such, the process 400 illustrates processing to rank individualvertices of network graphs for label display based upon chosenmeta-properties (e.g., data significance) of the respective vertices anda 3D distance of the vertices from a viewpoint of the 3D graph. Theprocess 400 performs bi-modal hysteresis processing to manage displayand non-display of labels for the vertices. The process 400 iterativelyupdates the determined distance, the calculated ranking figure, and theranking of the vertices of the network graph responsive to one or moreuser inputs instructing a change of the 3D rendering of the networkgraph and any changes to the underlying data or meta-properties of thenetwork graph. The process 400 selectively displays labels on a displayfor an updated subset of the set of vertices as a function of theupdated ranking. The process 400 further manages real-time labelrendering budget during display frame refresh periods to displayadditional labels for candidate vertices, and randomizes the hysteresisof any candidate vertices that did not get labeled to improve bothreal-time processing of label rendering and to reduce label flickeraffects that may otherwise occur if multiple labels were caused to berendered or not rendered during individual frame refresh periods.

Some embodiments of the present invention may improve the technology ofcomputers in one, or more, of the following ways: (i)reducing/preventing label rendering loop timing violations relative todisplay refresh time intervals; (ii) improving achieved displayrendering frame rate for label rendering of network graphs; (iii)increasing speed of display update processing; (iv) reducing/preventingstuttered/jerky display updates; (v) reducing computations required toselect labels to render; (vi) improving rendered output by reducingbrowser label overload and clutter; and (vii) improving user interfaceoutput processing.

The present invention is not abstract because it relates particularly tocomputer operations and/or hardware for reasons that may include thefollowing: (i) real-time performance improvement of computers fordisplay refresh processing; (ii) processor cycle reduction of computerprocessing during display output generation; (iii) improvement ofautonomous computer data selection processing for determining whichvertices and edges to process for label generation; and (iv) automatedadjustment to increase or decrease quantities of selected verticesand/or edges for which to display/output labels according to availablereal-time frame rate processing cycles.

As described above in association with FIG. 1 through FIG. 4B, theexample systems and processes provide adaptive labeling of networkgraphs. Many other variations and additional activities associated withadaptive labeling of network graphs are possible and all are consideredwithin the scope of the present subject matter.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a,” “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the art basedupon the teachings herein without departing from the scope and spirit ofthe invention. The subject matter was described to explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

What is claimed is:
 1. A computer-implemented method, comprising: by aprocessor, for each vertex of a network graph that comprises a pluralityof vertices: determining a meta-property of the vertex relative to othervertices of the plurality of vertices; determining a distance of thevertex from a point that approximates a user's viewpoint relative to arendering of the network graph; calculating a ranking figure based onthe square of the determined meta-property and the square of thedetermined distance; ranking the plurality of vertices of the networkgraph based on the calculated ranking figures; and selectivelydisplaying, labels for a subset of the plurality of vertices based onthe ranking.
 2. The computer-implemented method of claim 1, furthercomprising the processor dynamically updating which of the plurality ofvertices form the subset of the plurality of vertices for which labelsare selectively displayed responsive to real-time changes of themetaproperties of the plurality of vertices that result from real-timechanges in data represented by the respective vertices within thenetwork graph.
 3. The computer-implemented method of claim 1, furthercomprising the processor dynamically adjusting a proportion of theplurality of vertices for which the labels are selectively displayedaccording to a configured real-time computational performance criterionfor display update processing.
 4. The computer-implemented method ofclaim 1, further comprising the processor: establishing, as bi-modaldisplay output hysteresis: a first hysteresis phase that defines aminimum display time for displaying the labels for the subset of theplurality of vertices responsive to the labels being displayed; and asecond hysteresis phase that defines a minimum time for not displayingthe labels for any of the subset of the plurality of vertices responsiveto the display of the labels being stopped; and reducing real-time labeldisplay flicker, responsive to real-time changes of the metapropertiesof the plurality of vertices according to the bi-modal display outputhysteresis.
 5. The computer-implemented method of claim 1, furthercomprising the processor: monitoring an achieved real-time computationalperformance of display update processing, relative to a thresholdreal-time computational performance criterion for display updateprocessing, and one of: responsive to determining that the achievedreal-time computational performance exceeds the threshold real-timecomputational performance criterion for display update processing,increasing a proportion of the plurality of vertices for which thelabels are selectively displayed until the achieved real-timecomputational performance approximates the threshold real-timecomputational performance criterion; and responsive to determining thatthe achieved real-time computational performance is below the thresholdreal-time computational performance criterion for display updateprocessing, reducing the proportion of the plurality of vertices forwhich the labels are selectively displayed until the achieved real-timecomputational performance approximates the threshold real-timecomputational performance criterion.
 6. The computer-implemented methodof claim 1, further comprising the processor: iteratively updating thedetermined distance, the calculated ranking figure, and the ranking ofthe plurality of vertices of the network graph responsive to at leastone user input instructing a change of the rendering of the networkgraph; and selectively displaying, labels for an updated subset of theplurality of vertices based on the updated ranking.
 7. Thecomputer-implemented method of claim 1, where the processor calculatingthe ranking figure based on the determined meta-property and thedetermined distance comprises the processor for each vertex of thenetwork graph that comprises the plurality of vertices: calculating theranking figure as a square of the meta-property of the respective vertexdivided by a square of the determined distance of the vertex from thepoint that approximates the user's viewpoint relative to the renderingof the network graph.
 8. A system, comprising: a processor programmedto, for each vertex of a network graph that comprises a plurality ofvertices: determine a meta-property of the vertex relative to othervertices of the plurality of vertices; determine a distance of thevertex from a point that approximates a user's viewpoint relative to arendering of the network graph; calculate a ranking figure based on thesquare of the determined meta-property and the square of the determineddistance; rank the plurality of vertices of the network graph based onthe calculated ranking figures; and selectively display labels for asubset of the plurality of vertices based on the ranking.
 9. The systemof claim 8, where the processor is further programmed to dynamicallyupdate which of the plurality of vertices form the subset of theplurality of vertices for which labels are selectively displayedresponsive to real-time changes of the meta-properties of the pluralityof vertices that result from real-time changes in data represented bythe respective vertices within the network graph.
 10. The system ofclaim 8, where the processor is further programmed to dynamically adjusta proportion of the plurality of vertices for which the labels areselectively displayed according to a configured real-time computationalperformance criterion for display update processing.
 11. The system ofclaim 8, where the processor is further programmed to: establish, asbi-modal display output hysteresis: a first hysteresis phase thatdefines a minimum display time for displaying the labels for the subsetof the plurality of vertices responsive to the labels being displayed;and a second hysteresis phase that defines a minimum time for notdisplaying the labels for any of the subset of the plurality of verticesresponsive to the display of the labels being stopped; and reducereal-time label display flicker, responsive to real-time changes of themetaproperties of the plurality of vertices according to the bi-modaldisplay output hysteresis.
 12. The system of claim 8, where theprocessor is further programmed to: monitor an achieved real-timecomputational performance of display update processing, relative to athreshold real-time computational performance criterion for displayupdate processing, and one of: responsive to determining that theachieved real-time computational performance exceeds the thresholdreal-time computational performance criterion for display updateprocessing, increase a proportion of the plurality of vertices for whichthe labels are selectively displayed until the achieved real-timecomputational performance approximates the threshold real-timecomputational performance criterion; and responsive to determining thatthe achieved real-time computational performance is below the thresholdreal-time computational performance criterion for display updateprocessing, reduce the proportion of the plurality of vertices for whichthe labels are selectively displayed until the achieved real-timecomputational performance approximates the threshold real-timecomputational performance criterion.
 13. The system of claim 8, where,in being programmed to calculate the ranking figure based on thedetermined meta-property in combination with the determined distance,the processor is programmed to, for each vertex of the network graphthat comprises the plurality of vertices: calculate the ranking figureas a square of the meta-property of the respective vertex divided by asquare of the determined distance of the vertex from the point thatapproximates the user's viewpoint relative to the rendering of thenetwork graph on the display.
 14. A computer program product,comprising: a computer readable storage medium having computer readableprogram code embodied therewith, where the computer readable storagemedium is not a transitory signal per se and where the computer readableprogram code when executed on a computer causes the computer to, foreach vertex of a network graph that comprises a plurality of vertices:determine a meta-property of the vertex relative to other vertices ofthe plurality of vertices; determine a distance of the vertex from apoint that approximates a user's viewpoint relative to a rendering ofthe network graph; calculate a ranking figure based on the square of thedetermined square of the meta-property and the square of the determineddistance; rank the plurality of vertices of the network graph based onthe calculated ranking figures; and selectively display, labels for asubset of the plurality of vertices based on the ranking.
 15. Thecomputer program product of claim 14, where the computer readableprogram code when executed on the computer further causes the computerto dynamically update which of the plurality of vertices form the subsetof the plurality of vertices for which labels are selectively displayedresponsive to real-time changes of the meta-properties of the pluralityof vertices that result from real-time changes in data represented bythe respective vertices within the network graph.
 16. The computerprogram product of claim 14, where the computer readable program codewhen executed on the computer further causes the computer to dynamicallyadjust a proportion of the plurality of vertices for which the labelsare selectively displayed according to a configured real-timecomputational performance criterion for display update processing. 17.The computer program product of claim 14, where the computer readableprogram code when executed on the computer further causes the computerto: establish, as bi-modal display output hysteresis: a first hysteresisphase that defines a minimum display time for displaying the labels forthe subset of the plurality of vertices responsive to the labels beingdisplayed; a second hysteresis phase that defines a minimum time for notdisplaying the labels for any of the subset of the plurality of verticesresponsive to the display of the labels being stopped; and reducereal-time label display flicker, responsive to real-time changes of themetaproperties of the plurality of vertices according to the bi-modaldisplay output hysteresis.
 18. The computer program product of claim 14,where the computer readable program code when executed on the computerfurther causes the computer to: monitor an achieved real-timecomputational performance of display update processing, relative to athreshold real-time computational performance criterion for displayupdate processing, and one of: responsive to determining that theachieved real-time computational performance exceeds the thresholdreal-time computational performance criterion for display updateprocessing, increase a proportion of the plurality of vertices for whichthe labels are selectively displayed until the achieved real-timecomputational performance approximates the threshold real-timecomputational performance criterion; and responsive to determining thatthe achieved real-time computational performance is below the thresholdreal-time computational performance criterion for display updateprocessing, reduce the proportion of the plurality of vertices for whichthe labels are selectively displayed until the achieved real-timecomputational performance approximates the threshold real-timecomputational performance criterion.
 19. The computer program product ofclaim 14, where the computer readable program code when executed on thecomputer further causes the computer to: iteratively update thedetermined distance, the calculated ranking figure, and the ranking ofthe plurality of vertices of the network graph responsive to at leastone user input instructing a change of the rendering of the networkgraph; and selectively display, labels for an updated subset of theplurality of vertices based on the updated ranking.
 20. The computerprogram product of claim 14, where in causing the computer to calculatethe ranking figure based on the determined meta-property in combinationwith the determined distance, the computer readable program code whenexecuted on the computer causes the computer to, for each vertex of thenetwork graph that comprises the plurality of vertices: calculate theranking figure as a square of the meta-property of the respective vertexdivided by a square of the determined distance of the vertex from thepoint that approximates the user's viewpoint relative to the renderingof the network graph.